Dynamical analysis of a stochastic delayed SIR epidemic model with vertical transmission and vaccination

Zhang, Xiaolei; Liu, Maoxing

doi:10.1186/s13662-022-03707-7

Cited by 6 publications

(1 citation statement)

References 43 publications

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“…When it comes to stochastic epidemic models incorporating the ineffectiveness of vaccination, most of the current research works neglect the dynamics of the vaccinated population, and make use of time delays to take into consideration the duration elapsed before the effectiveness of the vaccine wears off. In this context, we mention for instance the results presented in [ 28 , 29 ]. Another limitation of the aforementioned works is assuming that the immunity can be gained solely after one stage of vaccination.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a stochastic non-autonomous SVIR model with multiple stages of vaccination

Mehdaoui

Alaoui

Tilioua

2022

J. Appl. Math. Comput.

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In this paper, we analyze the dynamics of a new proposed stochastic non-autonomous SVIR model, with an emphasis on multiple stages of vaccination, due to the vaccine ineffectiveness. The parameters of the model are allowed to depend on time, to incorporate the seasonal variation. Furthermore, the vaccinated population is divided into three subpopulations, each one representing a different stage. For the proposed model, we prove the mathematical and biological well-posedness. That is, the existence of a unique global almost surely positive solution. Moreover, we establish conditions under which the disease vanishes or persists. Furthermore, based on stochastic stability theory and by constructing a suitable new Lyapunov function, we provide a condition under which the model admits a non-trivial periodic solution. The established theoretical results along with the performed numerical simulations exhibit the effect of the different stages of vaccination along with the stochastic Gaussian noise on the dynamics of the studied population.

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a stochastic non-autonomous SVIR model with multiple stages of vaccination

Mehdaoui

Alaoui

Tilioua

2022

J. Appl. Math. Comput.

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A delayed deterministic and stochastic SIRICV model: Hopf bifurcation and stochastic analysis

Hajri

Allali

Amine

2024

Mathematics and Computers in Simulation

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Stability analysis of an SIR epidemic model with homestead-isolation on the susceptible and infectious, immunity, relapse and general incidence rate

Bernoussi¹

2022

Int. J. Biomath.

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In this paper, we propose the global dynamics of an SIR epidemic model with distributed latent period, immunity, relapse, homestead-isolation of the susceptible and infectious individuals and general incidence rate. The resulting model has a disease-free equilibrium and if [Formula: see text] then the SIR epidemic model admits a unique endemic equilibrium. By using suitable Lyapunov functionals and LaSalle’s invariance principle, the global stability of the disease-free equilibrium and the endemic equilibrium is established, under suitable monotonicity conditions on the incidence function.

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Dynamical analysis of a stochastic delayed SIR epidemic model with vertical transmission and vaccination

Cited by 6 publications

References 43 publications

Dynamical analysis of a stochastic non-autonomous SVIR model with multiple stages of vaccination

Dynamical analysis of a stochastic non-autonomous SVIR model with multiple stages of vaccination

A delayed deterministic and stochastic SIRICV model: Hopf bifurcation and stochastic analysis

Stability analysis of an SIR epidemic model with homestead-isolation on the susceptible and infectious, immunity, relapse and general incidence rate

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